Modularity of the Rankin
نویسندگان
چکیده
In memory of my father Sundaram Ramakrishnan (SRK) Contents 1. Introduction 2. Notation and preliminaries 3. Construction of ⊠ : A(GL(2)) × A(GL(2)) → A(GL(4)) 3.1. Relevant objects and the strategy 3.2. Weak to strong lifting, and the cuspidality criterion 3.3. Triple product L-functions: local factors and holomorphy 3.4. Boundedness in vertical strips 3.5. Modularity in the good case 3.6. A descent criterion 3.7. Modularity in the general case 4. Applications 4.1. A multiplicity one theorem for SL(2) 4.2. Some new functional equations 4.3. Root numbers and representations of orthogonal type 4.4. Triple product L-functions revisited 4.5. The Tate conjecture for 4-fold products of modular curves
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